The present invention relates generally to imaging using cone beam scanning. More specifically, it relates to such tomographic imaging using asymmetric grids corresponding to non-square rectangular or other non-square detector elements.
In conventional computerized tomography (CT) for both medical and industrial applications, an x-ray fan beam and a linear array detector are used. Two-dimensional (2D) imaging is achieved. While the data set may be complete and image quality is correspondingly high, only a signal slice of an object is imaged at a time. When a 3D image is required, a stack of slices approach is employed. Acquiring a 3D data set one 2D slice at a time is inherently slow. Moreover, in medical applications, motion artifacts occur because adjacent slices are not imaged simultaneously. Also, dose utilization is less than optimal because the distance between slices is typically less than the x-ray collimator aperture, resulting in double exposure to many parts of the body. In 2D CT, the scanning path of the source is often a simply circular scan about the object. The linear array detector is fixed relative to the source. (Although it is usually to talk about a scan path of a source relative to the object to be imaged, it is to be appreciated that the object may be rotated or otherwise moved to provide relative motion between the object and the source.)
In a system employing true cone beam geometry for 3D imaging, a cone beam x-ray source and a 2D area detector are used. An object is scanned, preferably over a 360.degree. angular range, either by moving the x-ray source in a scanning circle about the object or by rotating the object while the source remains stationary. In either case, the area detector is fixed relative to the source. The relative movement between the source and object which is to be imaged provides scanning in either case. Compared to the conventional 2D stack of slices approach to achieve 3D imaging, the cone beam geometry has the potential to achieve rapid 3D imaging of both medical and industrial objects with improved dose utilization.
The 3D CT imaging generally uses a Radon transform approach. (Radon transforms are also used in 2D CT.) The object is defined in terms of its x-ray attenuation coefficient. The measured cone beam projection data corresponds to a line integral of this function over the radial direction from the radiation source to a particular detector element within the detector array. The 3D Radon transform of an object at a point is given by the area integral of the x-ray attenuation coefficient over the plane passing through the point, which plane is perpendicular to the line from the origin to the particular point. If parallel beams of x-rays are applied to the object which is to be imaged, line integrals of the detector data are equal to the Radon transform of the object. However, obtaining the Radon transform is significantly more complex where a cone beam of x-ray or other imaging energy is applied to the object. In that case, obtaining the Radon transform, also called Radon data, is significantly more difficult. Once Radon data is obtained, an inverse Radon transformation is used to convert the Radon data into a reconstructed image which is then displayed.
The present inventor's previous application U.S. Pat. No. 5,257,183, incorporated by reference above, discloses a technique for calculating the radial derivative of Radon data from cone beam data. The present inventor's incorporated by reference application Ser. No. 07/631,818 discloses a technique for inverting the Radon data to obtain the reconstructed image of the object which is being viewed. In order to perform the Radon inversion, Radon data (as opposed to derivatives of Radon data) is required (except where using those few processors which perform Radon inversion using derivative data) and the Radon data should reside on polar grids on a number of predetermined vertical planes containing the z axis as the common axis. These requirements arise because the first part of the Radon inversion process is a two dimensional (2D) CT image reconstruction on each vertical plane, which takes input data in the form of Radon data at equally spaced angle .theta. and equally spaced detector spacings s. However, the technique of the referenced 07/631,815 application initially produces radial derivatives of the Radon data, instead of Radon data itself, and the derivative data is generated on a spherical shell having as its diameter a line segment SO connection a source position S and an origin O (instead of being generated on the points of the polar grids). The U.S. Pat. No. 5,257,183 application further describes techniques for converting from the radial derivative of Radon data to Radon data itself and to obtain the Radon data on the polar grid points by use of the Radon data relative to the spherical shell, often called the Radon shell. However, the calculation of Radon data over the spherical Radon shell requires a relatively large amount of processing or computational power. Further, using that Radon data to provide Radon data at the points on the polar grid of the vertical planes requires relatively complex techniques which, in effect, involve interpolation of different data points on the Radon shell over the shell. This three-dimensional (3D) interpolation is relatively complex and accordingly requires large amounts of computational power.
The present inventor's previous application Ser. No. 08/100,818, incorporated by reference above, provides for the simplification of the generation of Radon data.
The three incorporated by reference applications generally provide techniques allowing reconstruction of images using projection data. However, these and other reconstruction techniques (whether used for two-dimensional imaging or three-dimensional imaging) generally encounter problems when applied to asymmetric grids such as correspond to non-square rectangular or other non-square detector elements. For example, rectangular detectors which are not square could be used to provide better resolution in one dimension than in another dimension, this commonly being advantageous in medical imaging of a patient.
The problems with use of asymmetric grids will be better understood by initially realizing that tomography involves reconstruction of images from data collected at a number of angles. Common image reconstruction procedures are designed with symmetric geometry in mind. In two-dimensional (2D) computerized tomography (CT) images are usually reconstructed on a square grid with square grid elements. With symmetric geometry the various operations in image reconstruction, notably backprojection, can be carried out in the same manner at all the angles, resulting in uniform image quality and ease of operation.
Some situations make asymmetric geometry advantageous. For example, it is sometimes desirable to image an object with slice thickness larger than the later resolutions when using three-dimensional CT. Under such circumstances, the detector elements used in the area detector are usually non-square rectangular in shape, with their lateral and vertical dimensions determined by the corresponding detector element resolutions. The asymmetric voxel (the rectangular box on the grid) dimensions and detector element dimensions introduce complications in the image reconstruction operations and potentially non-uniform image quality.